Analysis of m sets of symbolic interval variables.
Abstract
This work presents a new approach to analyze a series of m n p
tables X(1); : : : ;X(m) of symbolic interval variables. In this new approach, we
firstly define a space of intervals with laws of composition ;
1; . This
allows extending this reasoning to the matrices of intervals. Then, we define a
n p compromise matrix X = Xiji=1;:::;n; j=1;:::;p; of type intervals, a measure
of covariance between interval variables, a new measure of correlation
between interval variables and the product operator
2 between a matrix n p
of intervals and one p vector u. This way, we achieve a symbolic PCA of compromise.
To express the variability of tables X(1); : : : ;X(m), they are projected
on the principal axes of PCA of intervals of compromise. For the interpretation
of factorial map, a new measure of correlation will be used.